Homework SourseShow that fx x4 5x 1 has a zero in the interval 01Solutio
Show that f(x) = x^4 - 5x + 1 has a zero in the interval [0,1].![Show that f(x) = x^4 - 5x + 1 has a zero in the interval [0,1].Solutiongiven f(x) = x^4 -5x+1 and interval [0,1] f(0) = 0^4- 5 .0 +1 = 1 f(1) = 1^4- 5.1 +1 = -](/WebImages/32/show-that-fx-x4-5x-1-has-a-zero-in-the-interval-01solutio-1092714-1761575634-0.webp "Show that f(x) = x^4 - 5x + 1 has a zero in the interval [0,1].Solutiongiven f(x) = x^4 -5x+1 and interval [0,1] f(0) = 0^4- 5 .0 +1 = 1 f(1) = 1^4- 5.1 +1 = -")
Solution
given f(x) = x^4 -5x+1 and interval [0,1]
f(0) = 0^4- 5 .0 +1 = 1
f(1) = 1^4- 5.1 +1 = -3
Since it verifies the intermediate value theorem, there is at least one c that belongs to the interval (0, 1) and intersects the x-axis and f(x) has a zero in the interval[0,1].
